%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUM503+1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:57:35 PM UTC 2026
% Result : Theorem 7.11s 4.80s
% Output : CNFRefutation 7.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 30
% Syntax : Number of formulae : 210 ( 58 unt; 0 def)
% Number of atoms : 700 ( 270 equ)
% Maximal formula atoms : 28 ( 3 avg)
% Number of connectives : 808 ( 318 ~; 381 |; 74 &)
% ( 3 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 205 ( 0 sgn 90 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(mMonAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != X2
& sdtlseqdt0(X1,X2) )
=> ! [X3] :
( aNaturalNumber0(X3)
=> ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
& sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
& sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
& sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonAdd) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2287,hypothesis,
( xn != xp
& sdtlseqdt0(xn,xp)
& xm != xp
& sdtlseqdt0(xm,xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mDefLE,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& sdtpldt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mDivSum,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,X3) )
=> doDivides0(X1,sdtpldt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivSum) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).
fof(mZeroAdd,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtpldt0(X1,X2) = sz00
=> ( X1 = sz00
& X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
fof(m__,conjecture,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMonMul,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( X1 != sz00
& X2 != X3
& sdtlseqdt0(X2,X3) )
=> ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
& sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
& sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETotal) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__2389,hypothesis,
sdtlseqdt0(xp,xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(m__2075,hypothesis,
~ sdtlseqdt0(xp,xm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__2315,hypothesis,
~ ( xk = sz00
| xk = sz10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).
fof(c_0_30,plain,
! [X145,X146,X148] :
( ( aNaturalNumber0(esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( X146 = sdtasdt0(X145,esk2_2(X145,X146))
| ~ doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) )
& ( ~ aNaturalNumber0(X148)
| X146 != sdtasdt0(X145,X148)
| doDivides0(X145,X146)
| ~ aNaturalNumber0(X145)
| ~ aNaturalNumber0(X146) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
fof(c_0_31,plain,
! [X91,X92] :
( ~ aNaturalNumber0(X91)
| ~ aNaturalNumber0(X92)
| aNaturalNumber0(sdtasdt0(X91,X92)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
fof(c_0_32,plain,
! [X149,X150,X151] :
( ( aNaturalNumber0(X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( X150 = sdtasdt0(X149,X151)
| X151 != sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) )
& ( ~ aNaturalNumber0(X151)
| X150 != sdtasdt0(X149,X151)
| X151 = sdtsldt0(X150,X149)
| X149 = sz00
| ~ doDivides0(X149,X150)
| ~ aNaturalNumber0(X149)
| ~ aNaturalNumber0(X150) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
cnf(c_0_33,plain,
( doDivides0(X3,X2)
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_34,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_35,plain,
! [X104] :
( ( sdtasdt0(X104,sz10) = X104
| ~ aNaturalNumber0(X104) )
& ( X104 = sdtasdt0(sz10,X104)
| ~ aNaturalNumber0(X104) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_36,plain,
! [X134,X135,X136] :
( ( sdtpldt0(X136,X134) != sdtpldt0(X136,X135)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X136,X134),sdtpldt0(X136,X135))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtpldt0(X134,X136) != sdtpldt0(X135,X136)
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) )
& ( sdtlseqdt0(sdtpldt0(X134,X136),sdtpldt0(X135,X136))
| ~ aNaturalNumber0(X136)
| X134 = X135
| ~ sdtlseqdt0(X134,X135)
| ~ aNaturalNumber0(X134)
| ~ aNaturalNumber0(X135) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])]) ).
cnf(c_0_37,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_38,plain,
( doDivides0(X1,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_40,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_41,plain,
( sdtlseqdt0(sdtpldt0(X1,X2),sdtpldt0(X1,X3))
| X2 = X3
| ~ aNaturalNumber0(X1)
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,hypothesis,
sdtlseqdt0(xm,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_43,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_44,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_45,hypothesis,
xm != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
fof(c_0_46,plain,
! [X98] :
( ( sdtpldt0(X98,sz00) = X98
| ~ aNaturalNumber0(X98) )
& ( X98 = sdtpldt0(sz00,X98)
| ~ aNaturalNumber0(X98) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
fof(c_0_47,plain,
! [X117,X118] :
( ~ aNaturalNumber0(X117)
| ~ aNaturalNumber0(X118)
| sdtasdt0(X117,X118) != sz00
| X117 = sz00
| X118 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_48,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_49,plain,
( doDivides0(sz10,X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40])]) ).
cnf(c_0_50,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_51,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
fof(c_0_52,plain,
! [X129,X130,X131] :
( ~ aNaturalNumber0(X129)
| ~ aNaturalNumber0(X130)
| ~ aNaturalNumber0(X131)
| ~ sdtlseqdt0(X129,X130)
| ~ sdtlseqdt0(X130,X131)
| sdtlseqdt0(X129,X131) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_53,hypothesis,
( sdtlseqdt0(sdtpldt0(X1,xm),sdtpldt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]),c_0_45]) ).
cnf(c_0_54,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_55,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_56,plain,
! [X119,X120,X122] :
( ( aNaturalNumber0(esk1_2(X119,X120))
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( sdtpldt0(X119,esk1_2(X119,X120)) = X120
| ~ sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) )
& ( ~ aNaturalNumber0(X122)
| sdtpldt0(X119,X122) != X120
| sdtlseqdt0(X119,X120)
| ~ aNaturalNumber0(X119)
| ~ aNaturalNumber0(X120) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])]) ).
fof(c_0_57,plain,
! [X89,X90] :
( ~ aNaturalNumber0(X89)
| ~ aNaturalNumber0(X90)
| aNaturalNumber0(sdtpldt0(X89,X90)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_58,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,plain,
( sdtasdt0(sz10,sdtsldt0(X1,sz10)) = X1
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_40])]),c_0_50]) ).
cnf(c_0_60,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_61,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_62,hypothesis,
sdtlseqdt0(sdtpldt0(sz00,xm),xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]),c_0_43])]) ).
cnf(c_0_63,plain,
( sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| sdtpldt0(X2,X1) != X3
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
( aNaturalNumber0(sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_65,plain,
( sdtsldt0(sz00,sz10) = sz00
| ~ aNaturalNumber0(sdtsldt0(sz00,sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_40])]),c_0_50])]),c_0_55])]) ).
cnf(c_0_66,plain,
( aNaturalNumber0(sdtsldt0(X1,sz10))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_49]),c_0_40])]),c_0_50]) ).
cnf(c_0_67,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(sdtpldt0(sz00,xm))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_43])]) ).
cnf(c_0_68,plain,
( sdtlseqdt0(X1,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_63]),c_0_64]) ).
fof(c_0_69,plain,
! [X99,X100] :
( ~ aNaturalNumber0(X99)
| ~ aNaturalNumber0(X100)
| sdtasdt0(X99,X100) = sdtasdt0(X100,X99) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_70,plain,
sdtsldt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_55])]) ).
cnf(c_0_71,hypothesis,
( sdtlseqdt0(sz00,xp)
| ~ aNaturalNumber0(sdtpldt0(sz00,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_55]),c_0_44])]) ).
cnf(c_0_72,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_73,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_74,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_75,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
fof(c_0_76,plain,
! [X155,X156,X157] :
( ~ aNaturalNumber0(X155)
| ~ aNaturalNumber0(X156)
| ~ aNaturalNumber0(X157)
| ~ doDivides0(X155,X156)
| ~ doDivides0(X155,X157)
| doDivides0(X155,sdtpldt0(X156,X157)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivSum])]) ).
cnf(c_0_77,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_70]),c_0_55])]) ).
cnf(c_0_78,plain,
( sdtpldt0(X1,esk1_2(X1,X2)) = X2
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_79,hypothesis,
sdtlseqdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_54]),c_0_44])]) ).
cnf(c_0_80,plain,
( aNaturalNumber0(esk1_2(X1,X2))
| ~ sdtlseqdt0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_81,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_82,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_83,hypothesis,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_74]),c_0_44])]) ).
cnf(c_0_84,hypothesis,
( aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm)))
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_72]),c_0_43])]) ).
cnf(c_0_85,plain,
( doDivides0(X1,sdtpldt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_76]) ).
cnf(c_0_86,plain,
doDivides0(sz10,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_77]),c_0_40]),c_0_55])]) ).
fof(c_0_87,plain,
! [X93,X94] :
( ~ aNaturalNumber0(X93)
| ~ aNaturalNumber0(X94)
| sdtpldt0(X93,X94) = sdtpldt0(X94,X93) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_88,hypothesis,
sdtpldt0(sz00,esk1_2(sz00,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_43]),c_0_55])]) ).
cnf(c_0_89,hypothesis,
aNaturalNumber0(esk1_2(sz00,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_79]),c_0_43]),c_0_55])]) ).
cnf(c_0_90,hypothesis,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_73]),c_0_74]),c_0_44])]) ).
fof(c_0_91,plain,
! [X101,X102,X103] :
( ~ aNaturalNumber0(X101)
| ~ aNaturalNumber0(X102)
| ~ aNaturalNumber0(X103)
| sdtasdt0(sdtasdt0(X101,X102),X103) = sdtasdt0(X101,sdtasdt0(X102,X103)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
cnf(c_0_92,hypothesis,
( sdtasdt0(xp,esk2_2(xp,sdtasdt0(xm,xn))) = sdtasdt0(xm,xn)
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_43])]) ).
cnf(c_0_93,hypothesis,
aNaturalNumber0(esk2_2(xp,sdtasdt0(xn,xm))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_34]),c_0_44]),c_0_74])]) ).
cnf(c_0_94,plain,
( doDivides0(sz10,sdtpldt0(X1,sz00))
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_55]),c_0_40])]),c_0_49]) ).
cnf(c_0_95,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_87]) ).
cnf(c_0_96,hypothesis,
esk1_2(sz00,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_88]),c_0_89])]) ).
cnf(c_0_97,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_83]),c_0_90]),c_0_43])]) ).
fof(c_0_98,plain,
! [X115,X116] :
( ( X115 = sz00
| sdtpldt0(X115,X116) != sz00
| ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116) )
& ( X116 = sz00
| sdtpldt0(X115,X116) != sz00
| ~ aNaturalNumber0(X115)
| ~ aNaturalNumber0(X116) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).
cnf(c_0_99,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_100,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_101,hypothesis,
sdtasdt0(xp,esk2_2(xp,sdtasdt0(xm,xn))) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_34]),c_0_74]),c_0_44])]) ).
cnf(c_0_102,hypothesis,
aNaturalNumber0(esk2_2(xp,sdtasdt0(xm,xn))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_73]),c_0_44]),c_0_74])]) ).
cnf(c_0_103,plain,
( doDivides0(sz10,sdtpldt0(sz00,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_55])]) ).
cnf(c_0_104,hypothesis,
sdtpldt0(sz00,xp) = xp,
inference(rw,[status(thm)],[c_0_88,c_0_96]) ).
cnf(c_0_105,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_34]),c_0_74]),c_0_44])]) ).
cnf(c_0_106,plain,
( X1 = sz00
| sdtpldt0(X1,X2) != sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_107,hypothesis,
sdtpldt0(xm,esk1_2(xm,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_108,hypothesis,
aNaturalNumber0(esk1_2(xm,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_42]),c_0_43]),c_0_44])]) ).
cnf(c_0_109,plain,
( X1 = sdtsldt0(X2,X3)
| X3 = sz00
| ~ aNaturalNumber0(X1)
| X2 != sdtasdt0(X3,X1)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_110,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_40])]),c_0_34]) ).
cnf(c_0_111,hypothesis,
( sdtasdt0(xp,sdtasdt0(esk2_2(xp,sdtasdt0(xm,xn)),X1)) = sdtasdt0(sdtasdt0(xm,xn),X1)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_43])]),c_0_102])]) ).
cnf(c_0_112,hypothesis,
doDivides0(sz10,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_43])]) ).
fof(c_0_113,negated_conjecture,
~ ( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_114,plain,
! [X137,X138,X139] :
( ( sdtasdt0(X137,X138) != sdtasdt0(X137,X139)
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtlseqdt0(sdtasdt0(X137,X138),sdtasdt0(X137,X139))
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtasdt0(X138,X137) != sdtasdt0(X139,X137)
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) )
& ( sdtlseqdt0(sdtasdt0(X138,X137),sdtasdt0(X139,X137))
| X137 = sz00
| X138 = X139
| ~ sdtlseqdt0(X138,X139)
| ~ aNaturalNumber0(X137)
| ~ aNaturalNumber0(X138)
| ~ aNaturalNumber0(X139) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul])])]) ).
cnf(c_0_115,hypothesis,
( xp = sz00
| doDivides0(xm,sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_105]),c_0_44]),c_0_74])]) ).
cnf(c_0_116,hypothesis,
( xp = sz00
| aNaturalNumber0(sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_105]),c_0_74]),c_0_44])]) ).
cnf(c_0_117,hypothesis,
( xm = sz00
| xp != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_44])]) ).
cnf(c_0_118,plain,
( sdtsldt0(sdtasdt0(X1,X2),X1) = X2
| X1 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_109]),c_0_34]),c_0_38]) ).
fof(c_0_119,plain,
! [X132,X133] :
( ( X133 != X132
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) )
& ( sdtlseqdt0(X133,X132)
| sdtlseqdt0(X132,X133)
| ~ aNaturalNumber0(X132)
| ~ aNaturalNumber0(X133) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_120,hypothesis,
sdtasdt0(sdtasdt0(xm,xn),sz10) = sdtasdt0(xm,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_101]),c_0_102]),c_0_43]),c_0_40])]) ).
cnf(c_0_121,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_83]),c_0_90]),c_0_43])]) ).
cnf(c_0_122,hypothesis,
sdtasdt0(sz10,esk2_2(sz10,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_112]),c_0_40]),c_0_43])]) ).
cnf(c_0_123,hypothesis,
aNaturalNumber0(esk2_2(sz10,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_112]),c_0_43]),c_0_40])]) ).
fof(c_0_124,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(fof_nnf,[status(thm)],[c_0_113]) ).
cnf(c_0_125,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| X1 = sz00
| X2 = X3
| ~ sdtlseqdt0(X2,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_126,hypothesis,
sdtlseqdt0(xn,xp),
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_127,hypothesis,
xn != xp,
inference(split_conjunct,[status(thm)],[m__2287]) ).
cnf(c_0_128,hypothesis,
( sdtasdt0(xm,sdtsldt0(sdtasdt0(xp,xk),xm)) = sdtasdt0(xp,xk)
| xm = sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_115]),c_0_44])]),c_0_116]),c_0_117]) ).
cnf(c_0_129,hypothesis,
( sdtsldt0(sdtasdt0(xp,xk),xm) = xn
| xm = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_105]),c_0_44]),c_0_74])]),c_0_117]) ).
cnf(c_0_130,hypothesis,
( sdtlseqdt0(X1,xp)
| ~ sdtlseqdt0(X1,xm)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_54]),c_0_44])]) ).
cnf(c_0_131,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_132,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X2,sdtasdt0(X1,X3))
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_100,c_0_73]) ).
cnf(c_0_133,hypothesis,
( sdtasdt0(sdtasdt0(xp,xk),sz10) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_120,c_0_105]) ).
cnf(c_0_134,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_34]),c_0_74]),c_0_44])]) ).
cnf(c_0_135,hypothesis,
esk2_2(sz10,xp) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_122]),c_0_123])]) ).
cnf(c_0_136,negated_conjecture,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xm)
| sdtasdt0(xp,xm) = sdtasdt0(xp,xk)
| ~ sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_137,hypothesis,
( X1 = sz00
| sdtlseqdt0(sdtasdt0(X1,xn),sdtasdt0(X1,xp))
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_43]),c_0_74])]),c_0_127]) ).
cnf(c_0_138,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_139,plain,
( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
| X2 = sz00
| X1 = X3
| ~ sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_140,hypothesis,
( sdtlseqdt0(xm,X1)
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_44])]) ).
cnf(c_0_141,hypothesis,
( sdtasdt0(xk,sdtasdt0(xp,sz10)) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_40]),c_0_43])]),c_0_134]) ).
cnf(c_0_142,hypothesis,
sdtasdt0(sz10,xp) = xp,
inference(rw,[status(thm)],[c_0_122,c_0_135]) ).
fof(c_0_143,plain,
! [X127,X128] :
( ~ aNaturalNumber0(X127)
| ~ aNaturalNumber0(X128)
| ~ sdtlseqdt0(X127,X128)
| ~ sdtlseqdt0(X128,X127)
| X127 = X128 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_144,hypothesis,
sdtlseqdt0(xp,xk),
inference(split_conjunct,[status(thm)],[m__2389]) ).
cnf(c_0_145,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| sdtasdt0(xm,xn) = sdtasdt0(xp,xm)
| ~ sdtlseqdt0(sdtasdt0(xm,xn),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_73]),c_0_74]),c_0_44])]) ).
cnf(c_0_146,hypothesis,
( xm = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xm,xp)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_44])]) ).
cnf(c_0_147,hypothesis,
( xm = X1
| X2 = sz00
| sdtlseqdt0(sdtasdt0(xm,X2),sdtasdt0(X1,X2))
| sdtlseqdt0(X1,xp)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_44])]) ).
cnf(c_0_148,hypothesis,
( sdtasdt0(xk,xp) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_73]),c_0_142]),c_0_40]),c_0_43])]) ).
cnf(c_0_149,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_143]) ).
cnf(c_0_150,hypothesis,
( sdtpldt0(xp,esk1_2(xp,xk)) = xk
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_144]),c_0_43])]) ).
cnf(c_0_151,hypothesis,
( aNaturalNumber0(esk1_2(xp,xk))
| ~ aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_144]),c_0_43])]) ).
cnf(c_0_152,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xm = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm))
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[c_0_145,c_0_138]) ).
cnf(c_0_153,hypothesis,
( xm = sz00
| sdtlseqdt0(sdtasdt0(xp,xk),sdtasdt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_73]),c_0_43]),c_0_44])]) ).
cnf(c_0_154,hypothesis,
( xp = sz00
| xk = xm
| sdtlseqdt0(sdtasdt0(xm,xp),sdtasdt0(xp,xk))
| sdtlseqdt0(xk,xp) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_43])]),c_0_134]) ).
cnf(c_0_155,plain,
( sdtpldt0(X1,X2) = X1
| ~ sdtlseqdt0(sdtpldt0(X1,X2),X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_68]),c_0_64]) ).
cnf(c_0_156,hypothesis,
( sdtpldt0(xp,esk1_2(xp,xk)) = xk
| xp = sz00 ),
inference(spm,[status(thm)],[c_0_150,c_0_134]) ).
cnf(c_0_157,hypothesis,
( xp = sz00
| aNaturalNumber0(esk1_2(xp,xk)) ),
inference(spm,[status(thm)],[c_0_151,c_0_134]) ).
cnf(c_0_158,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xm = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_159,hypothesis,
( xk = xm
| xp = sz00
| sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk))
| sdtlseqdt0(xk,xp) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_73]),c_0_43]),c_0_44])]) ).
cnf(c_0_160,hypothesis,
( xp = sz00
| xk = xp
| ~ sdtlseqdt0(xk,xp) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_43])]),c_0_157]) ).
cnf(c_0_161,negated_conjecture,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xk = xm
| xm = sz00
| sdtlseqdt0(xk,xp) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_117]) ).
cnf(c_0_162,hypothesis,
( sdtasdt0(xp,xk) = sdtasdt0(xp,xm)
| xm = sz00
| xk = xm
| xk = xp ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_160,c_0_161]),c_0_117]) ).
fof(c_0_163,plain,
! [X105] :
( ( sdtasdt0(X105,sz00) = sz00
| ~ aNaturalNumber0(X105) )
& ( sz00 = sdtasdt0(sz00,X105)
| ~ aNaturalNumber0(X105) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_164,plain,
( doDivides0(X1,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_73]) ).
cnf(c_0_165,plain,
( sdtsldt0(sdtasdt0(X1,X2),X2) = X1
| X2 = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_118,c_0_73]) ).
cnf(c_0_166,hypothesis,
( sdtsldt0(sdtasdt0(xp,xm),xm) = xn
| xk = xp
| xk = xm
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_129,c_0_162]) ).
fof(c_0_167,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(fof_simplification,[status(thm)],[m__2075]) ).
cnf(c_0_168,plain,
( sz00 = sdtasdt0(sz00,X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_169,hypothesis,
doDivides0(xp,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_142]),c_0_43]),c_0_40])]) ).
cnf(c_0_170,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_163]) ).
cnf(c_0_171,hypothesis,
( xk = xm
| xk = xp
| xm = sz00 ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_44]),c_0_43])]),c_0_127]) ).
cnf(c_0_172,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_167]) ).
cnf(c_0_173,plain,
( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_168]),c_0_55])]) ).
cnf(c_0_174,hypothesis,
sdtasdt0(xp,esk2_2(xp,xp)) = xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_169]),c_0_43])]) ).
cnf(c_0_175,hypothesis,
aNaturalNumber0(esk2_2(xp,xp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_169]),c_0_43])]) ).
cnf(c_0_176,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_100]),c_0_55])]),c_0_34]) ).
cnf(c_0_177,hypothesis,
( xm = sz00
| xk = xp ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_171]),c_0_172]) ).
fof(c_0_178,plain,
! [X112,X113,X114] :
( ( sdtasdt0(X112,X113) != sdtasdt0(X112,X114)
| X113 = X114
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| X112 = sz00
| ~ aNaturalNumber0(X112) )
& ( sdtasdt0(X113,X112) != sdtasdt0(X114,X112)
| X113 = X114
| ~ aNaturalNumber0(X113)
| ~ aNaturalNumber0(X114)
| X112 = sz00
| ~ aNaturalNumber0(X112) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
cnf(c_0_179,hypothesis,
sdtasdt0(sz00,esk2_2(xp,xp)) = sdtasdt0(sz00,xp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_174]),c_0_175]),c_0_43])]) ).
cnf(c_0_180,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_72]),c_0_81]),c_0_43])]) ).
cnf(c_0_181,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_39]),c_0_40])]) ).
fof(c_0_182,hypothesis,
( xk != sz00
& xk != sz10 ),
inference(fof_nnf,[status(thm)],[m__2315]) ).
cnf(c_0_183,hypothesis,
sdtasdt0(sdtasdt0(xm,xn),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_111]),c_0_102]),c_0_43]),c_0_55])]) ).
cnf(c_0_184,hypothesis,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_101]),c_0_43])]),c_0_102])]) ).
cnf(c_0_185,negated_conjecture,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xp)
| xm = sz00
| ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xp)) ),
inference(spm,[status(thm)],[c_0_158,c_0_177]) ).
cnf(c_0_186,plain,
( X1 = sz00
| X2 = X3
| sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| sdtlseqdt0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(spm,[status(thm)],[c_0_125,c_0_131]) ).
cnf(c_0_187,plain,
( X1 = X3
| X2 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X3,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_178]) ).
cnf(c_0_188,hypothesis,
sdtasdt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_179]),c_0_175])]) ).
cnf(c_0_189,hypothesis,
( sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_34]),c_0_44]),c_0_74])]) ).
cnf(c_0_190,plain,
( sdtasdt0(X1,X2) = sz00
| X3 = sz00
| sdtasdt0(X1,sdtasdt0(X2,X3)) != sz00
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_100]),c_0_34]) ).
cnf(c_0_191,hypothesis,
( sdtasdt0(sz10,sdtasdt0(xp,xk)) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_105]),c_0_74]),c_0_44])]) ).
cnf(c_0_192,hypothesis,
xk != sz00,
inference(split_conjunct,[status(thm)],[c_0_182]) ).
cnf(c_0_193,hypothesis,
sdtasdt0(sz00,sdtasdt0(xm,xn)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_183]),c_0_55]),c_0_184])]) ).
cnf(c_0_194,negated_conjecture,
( sdtasdt0(xp,xm) = sdtasdt0(xp,xp)
| xm = sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_43]),c_0_44])]),c_0_45]),c_0_172]),c_0_117]) ).
cnf(c_0_195,hypothesis,
( xp = sz00
| sz00 = X1
| sdtasdt0(X1,xp) != sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_188]),c_0_43]),c_0_55])]) ).
cnf(c_0_196,hypothesis,
( sdtasdt0(sdtasdt0(xp,xk),X1) = sdtasdt0(xn,sdtasdt0(xm,X1))
| xp = sz00
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_189]),c_0_44]),c_0_74])]) ).
cnf(c_0_197,hypothesis,
( xp = sz00
| sdtasdt0(xp,xk) != sz00 ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_142]),c_0_43]),c_0_40])]),c_0_192]),c_0_134]) ).
cnf(c_0_198,hypothesis,
sdtasdt0(xm,sdtasdt0(xn,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_183]),c_0_55]),c_0_74]),c_0_44])]) ).
cnf(c_0_199,hypothesis,
sdtasdt0(sz00,xn) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_173]),c_0_74]),c_0_44])]) ).
cnf(c_0_200,hypothesis,
( sdtsldt0(sdtasdt0(xp,xp),xm) = xn
| xm = sz00 ),
inference(spm,[status(thm)],[c_0_129,c_0_177]) ).
cnf(c_0_201,negated_conjecture,
( sdtsldt0(sdtasdt0(xp,xp),xm) = xp
| xm = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_194]),c_0_44]),c_0_43])]) ).
cnf(c_0_202,hypothesis,
( xp = sz00
| sdtasdt0(xn,sdtasdt0(xm,xp)) != sz00 ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_195,c_0_196]),c_0_43])]),c_0_116]),c_0_197]) ).
cnf(c_0_203,hypothesis,
sdtasdt0(xm,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_73]),c_0_199]),c_0_55]),c_0_74])]) ).
cnf(c_0_204,hypothesis,
xm = sz00,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_127]) ).
cnf(c_0_205,hypothesis,
( xp = sz00
| sdtasdt0(xn,sdtasdt0(xp,xm)) != sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_202,c_0_73]),c_0_43]),c_0_44])]) ).
cnf(c_0_206,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_170]),c_0_55]),c_0_102])]),c_0_183]) ).
cnf(c_0_207,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_183,c_0_132]),c_0_55]),c_0_44]),c_0_74])]),c_0_203]) ).
cnf(c_0_208,hypothesis,
xp != sz00,
inference(rw,[status(thm)],[c_0_45,c_0_204]) ).
cnf(c_0_209,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_205,c_0_204]),c_0_206]),c_0_207])]),c_0_208]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM503+1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n018.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 00:39:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 7.11/4.80 % Version : CSE_E---1.7
% 7.11/4.80 % Problem : theBenchmark.p
% 7.11/4.80 % SZS status Theorem for theBenchmark.p
% 7.11/4.80 % SZS output start CNFRefutation
% See solution above
% 7.11/4.83 % Total time : 3.372s
%------------------------------------------------------------------------------